A single-intermediate-state (SIS) approximation is developed for dealing with the pairing Hamiltonian. With the aid of this approximation, expressions are obtained for the ground-state energy of an (n+2)-particle system in terms of the ground-state wave function of the n-particle system. Results are obtained for excited-state energies in the n- and (n±1)-particle systems. Numerical comparisons are made with reliable results obtained with other techniques. It is observed that the results obtained from the SIS approximation are quite accurate. The SIS approximation is also used to point out one source of error inherent in the BCS solution of the pairing problem. © 1968 The American Physical Society.
